Boundary perturbation solution for nearly circular holes and rigid inclusions in an infinite elastic medium

Journal of Applied Mechanics, Transactions ASME

Volumn 75, Issue 1, 2008, Pages 0110151-0110158

  Ekneligoda, Thushan C ^a   Zimmerman, Robert W ^a  

^a ROYAL INSTITUTE OF TECHNOLOGY   (Sweden)

Author keywords

Boundary perturbation; Cavities; Effective moduli; Rigid inclusions

Indexed keywords

COMPRESSIBILITY; CONCENTRATION (PROCESS); INCLUSIONS; NUMERICAL ANALYSIS; PERTURBATION TECHNIQUES; TWO DIMENSIONAL;

BOUNDARY ELEMENTS; BOUNDARY PERTURBATIONS; CIRCULAR HOLES; CORRESPONDENCE PRINCIPLE; DILUTE CONCENTRATIONS; EFFECTIVE BULK MODULUS; ELASTIC MEDIUM; FOURTH ORDER; HYDROSTATIC STRESSES; MUSKHELISHVILI; NUMERICAL VALUES; PORE COMPRESSIBILITY; RIGID INCLUSIONS; TWO-DIMENSIONAL (2D);

BOUNDARY ELEMENT METHOD;

EID: 47149098226     PISSN: 00218936     EISSN: None     Source Type: Journal    
DOI: 10.1115/1.2745826     Document Type: Article

References (32)

1. Mura, T., 1987, Micromechanics of Defects in Solids, 2nd ed., Kluwer, Amsterdam.
2. Nemat-Nasser. S., and Hori, M., 1999, Micromechanics: Overall Properties of Heterogeneous Materials, 2nd ed., North-Holland, Dordrecht, The Netherlands.
3. Eshelby, J. D., 1957, "The Determination of the Elastic Field of an Ellipsoidal Inclusion, and Related Problems," Proc. R. Soc. London, Ser. A. 241. pp. 376-396.
4. Savin, G. N., 1961. Stress Concentration Around Holes, Pergamon, Oxford, UK.
5. Muskhelishvili, N. I., 1963. Some Basic Problems of the Mathematical Theory of Elasticity, 2nd ed., Noordhoff, Groningen, The Netherlands.
6. Sisavath, S., Jing, X. D., and Zimmerman, R. W., 2001, "Laminar Flow Through Irregularly-Shaped Pores in Sedimentary Rocks," Transp. Porous Media, 45, pp. 41-62.
7. Tsukrov, I., and Novak, J., 2004, "Effective Elastic Properties of Solids With Two-Dimensional Inclusions of Irregular Shapes," Int. J. Solids Struct., 41, pp. 6905-6924.
8. Zimmerman, R. W., 1986, "Compressibility of Two-Dimensional Cavities of Various Shapes," ASME J. Appl. Mech., 53, pp. 500-504.
9. Ekneligoda, T. C., and Zimmerman, R. W., 2006, "Compressibility of Two-Dimensional Pores Having n-Fold Axes of Symmetry," Proc. R. Soc. London. Ser. A, 462, pp. 1933-1947.
10. Chang, C. S., and Conway, H. D., 1968, "A Parametric Study of the Complex Variable Method for Analyzing the Stresses in an Infinite Plate Containing a Rigid Rectangular Inclusion," Int. J. Solids Struct., 4, pp. 1057-1066.
11. Jasiuk, I., Chen, J., and Thorpe, M. F., 1994, "Elastic Moduli of Two Dimensional Materials With Polygonal and Elliptical Holes," Appl. Mech. Rev., 47(Supp 1), pp. 18-21.
12. Kachanov, M., Tsukrov, I., and Shafiro, B., 1994, "Effective Moduli of Solids With Cavities of Various Shapes," Appl. Mech. Rev., 47(Supp 1), pp. 152-174.
13. van Dyke, M., 1975, Perturbation Methods in Fluid Mechanics, Parabolic Press, Stanford, CA.
14. Low, E. F., and Chang, F. W., 1967, "Stress Concentrations Around Shaped Holes," J. Eng. Mech., 93, pp. 33-44.
15. Wang, C. H., and Chao, C. K., 2002, "On Perturbation Solutions for Nearly Circular Inclusion Problems in Plane Thermoelasticity," ASME J. Appl. Mech., 69, pp. 36-44.
16. Parnes, R., 1987, "The Boundary Perturbation Method in Elastostatics-Investigation of Higher-Order Effects and Accuracy of Solutions," J. Mec. Theor. Appl., 6, pp. 295-314.
17. Gao, H., 1990, "A Boundary Perturbation Analysis for Elastic Inclusions and Interfaces," Int. J. Solids Struct., 28, pp. 703-725.
18. Givoli, D., and Elishakoff, I. 1992, "Stress-Concentration at a Nearly Circular Hole With Uncertain Irregularities," ASME J. Appl. Mech., 59, pp. S65-S71.
19. Little, R. W., 1973, Elasticity, Prentice Hall, Englewood Cliffs, NJ.
20. Barber, J. R., 1992, Elasticity, Kluwer, Dordrecht, The Netherlands.
21. Jasiuk, I., 1995, Cavities vis-a-vis Rigid Inclusions: Elastic Moduli of Materials With Polygonal Inclusions," Int. J. Solids Struct., 32, pp. 407-422.
22. Dundurs, J., 1989, "Cavities vis-à-vis Rigid Inclusions and Some Related General Results in Plane Elasticity," ASME J. Appl. Mech., 56, pp. 786-790.
23. Goodier, J. N., 1933, "Concentration of Stress around Spherical and Cylindrical Inclusions and Flaws," Trans. ASME, 55, pp. 39-44.
24. Zimmerman, R. W., 1991, Compressibility of Sandstones, Elsevier, Amsterdam, The Netherlands.
25. Vigdergauz, S., 2006, "Cross Relations Between the Planar Elastic Moduli of Perforated Structures," ASME J. Appl. Mech., 73, pp. 163-166.
26. Martel, S. J., and Muller, J. R., 2000, "A Two-Dimensional Boundary Element Method for Calculating Elastic Gravitational Stresses in Slopes," Pure Appl. Geophys., 157, pp. 989-1007.
27. Crouch, S. L., and Starfield, A. M., 1983, Boundary Element Method in Solid Mechanics, Allen and Unwin, London, UK.
28. Gol'dshtein, R. V., and Entov, V. M. 1994, Qualitative Methods in Continuum Mechanics, Wiley, New York.
29. Hashin, Z., 1983, "Analysis of Composite Materials - a Survey," ASME J. Appl. Mech., 50, pp. 481-505.
30. Warren, N., 1973, "Theoretical Calculation of the Compressibility of Porous Media," J. Geophys. Res., 78, pp. 352-362.
31. Rice, R. W., 1998, Porosity of Ceramics, Marcel Dekker, New York.
32. Prokopiev, O., and Sevostianov, I., 2006, "On the Possibility of Approximation of Irregular Porous Microstructure by Isolated Spheroidal Pores," Int. J. Fract., 139, pp. 129-136.